Question

question 3 of 10 which of the following could be the ratio between the lengths of the two legs of a 30 - 60 - 90 triangle? check all that apply. a. $sqrt{2}:sqrt{2}$ b. $sqrt{2}:sqrt{3}$ c. $1:sqrt{2}$ d. $sqrt{3}:3$ e. $1:sqrt{3}$ f. $3:3sqrt{3}$

Explanation:

Step1: Recall 30 - 60 - 90 triangle side - ratio

In a 30 - 60 - 90 triangle, if the shorter leg (opposite 30°) is $a$, the longer leg (opposite 60°) is $a\sqrt{3}$, and the hypotenuse is $2a$. The ratio of the shorter leg to the longer leg is $1:\sqrt{3}$.

Step2: Simplify given ratios

• For D: $\sqrt{3}:3=\sqrt{3}: \sqrt{9}=1:\sqrt{3}$.
• For F: $3:3\sqrt{3}=1:\sqrt{3}$.

Answer:

D. $\sqrt{3}:3$, E. $1:\sqrt{3}$, F. $3:3\sqrt{3}$